Accuracy of a Bayesian technique to estimate position and activity of orphan gamma-ray sources by mobile gamma spectrometry: Influence of imprecisions in positioning systems and computational approximations

The purpose of this study was to investigate the effects of experimental data on performance of a developed Bayesian algorithm tailored for orphan source search, estimating which parameters affect the accuracy of the algorithm. The algorithm can estimate the position and activity of a gamma-ray point source from experimental mobile gamma spectrometry data. Bayesian estimates were made for source position and activity using mobile gamma spectrometry data obtained from one 123% HPGe detector and two 4-l NaI(Tl) detectors, considering angular variations in counting efficiency for each detector. The data were obtained while driving at 50 km/h speed past the sources using 1 s acquisition interval in the detectors. It was found that deviations in the recorded coordinates of the measurements can potentially increase the uncertainty in the position of the source 2 to 3 times and slightly decrease the activity estimations by about 7%. Due to the various sources of uncertainty affecting the experimental data, the maximum predicted relative deviations of the activity and position of the source remained about 30% regardless of the signal-to-noise ratio of the data. It was also found for the used vehicle speed of 50 km/h and 1 s acquisition time, that if the distance to the source is greater than the distance travelled by the detector during the acquisition time, it is possible to use point approximations of the count-rate function in the Bayesian likelihood with minimal deviations from the integrated estimates of the count-rate function. This approximation reduces the computational demands of the algorithm increasing the potential for applying this method in real-time orphan source search missions.

The comments: 1) In abstract, "This reduces the computational demands increasing the potential of real time applications of the method". Please re-write.
2) In line 9, "but gives no direct information on the distance to the source or its activity.", the detector is measuring some activity, it is better to refer to "actual activity" of the source, when addressing this.
3) In line 15, "with which", consider changing to "at which". 4) In line 47, "…orphan source the parameters of interest" add a comma after "source", please take care of the punctuation throughout the paper. There are many issues similar to what I pointed out here. 5) In lines 58-59, "vague prior is usually used", do you mean something like an initial guess? Please revise accordingly. 6) In line 59, "large variance", how do you defined this variance, statistically speaking "variance" would only be meaningful when we have a mean (refer to the formula). Please clarify briefly. 7) In lines 60-61, "However, if there is reason to believe that a radioactive source is in the area, it can be assumed that it could be anywhere in the area." Please re-phrase and re-write. 8) In line 64, "Similarly, a Gamma distribution with large shape and rate parameters…", this confusing to me, have you employed Gamma distribution in your model, or you just use this as an example since the distribution takes two parameters? Please clarify. 9) In line 106, "a set of arbitrary initial values of", by "arbitrary" do you mean "guess values"? please revised accordingly. 10) In line 110, "uniform random number between 0 and 1", how did you generate these random numbers? Was it produced sequentially in your model or it's an array? How did the seed changes in each iteration? Please explain briefly. 11) In line 126, please define "GNSS". 12) You have provided a schematic of the vehicle's path and source locations. It would be nice to get some pictures of your experimental setup, so that the readers can understand how detectors were setup in the vehicle. 13) In Fig. 1, please consider changing the symbol for source location from "" to something like a dot, as there will be lesser overlap between the symbols. 14) In line 149, "…at a steady speed of 50 km/h (13.9 m/s)", Please comment on the variations in the results as a result of changing the speed of the vehicle to some value other than 70 km/h. 15) In lines 149-150, "At least 7 complete passes of the sources were made for each experimental set-up.", how does driving 7 times pass the source reflect back on the realistic conditions, at which there will be an orphan source? Please comment.
16) In lines 157-158, the ROI was selected with the prior knowledge of the source that you have used in your experimentation. Please comment how does a lost and unknown source would effect the results and the methodology that you have employed here. 17) In Eq. (3), please define RDi.
18) It is understandable that you have considered the actual activity of the source to compute the degree of deviation in your results. Just to avoid confusion, please help add a statement that actual activity and position of the source does not need to be known when employing this method in realistic scenarios.

19)
In lines 217-218, "the usual speed of the vehicle is about 50 km/h combined with acquisition intervals of 1 s", please cite relevant papers to support this statement. 20) In line 234, the authors introduced "relative alignment", I am confused with it, please explain clearly. 21) In lines 244-246, is there any physical reason behind this variation? Please explain briefly. 22) In line 260, "despite regardless", remove "despite", revise accordingly. Check the punctuation as well. 23) Regarding the computational resources and the programming language used, will it be possible to parallelize your method to enhance the computational speed? Please comment briefly. 24) In line 284, what do you mean by "adjacent measurement coordinates"? 25) In line 293-294, "…correct values of the recorded count rate would be assigned incorrect coordinates…", please re-write and rephrase. Fig. 7, please explain why the SNR values for different detector and experiments is lower for Co-60 when compared to Cs-137? 27) I am confused about the trends of the lines shown for different quantile in Fig. 11. I am assuming parameters a and b are those used in Eq. (5), from the reported values shown in the figure, I guess there might be a mistake, unless I am misunderstanding something here. Let us consider Fig. 11, SNR values keep increasing on the x-axis (i.e., only positive values), linear or log-scale. Using Eq. (5), and setting x from 1 to 150, for 50% curve you have reported a = -8.3 and b = 0.012. However, I guess the b value should also be negative for the curve to start increasing as shown in your figures. See Fig. 1 below. For your reference, here is the simple code for this test; program main implicit none integer :: i,class real*8 :: y,x,a,b ! compile with Gfortran ! command ->> "gfortran main.f90" ! "./a.out" to run the program ! choose the case 1, 2 or 3 ! plot out.dat open(100, file='out.dat') print*, "enter case number (1) 28) The conclusion section is okay. However, please add some of the practical limitations that you have faced during your experimentation. It would be really useful for the readers to know all these.